Question

Write an equation for the nth term of the arithmetic sequence −15, −33, −51, −69, .... An equation for the nth term of the

Answer 1

Given:

The arithmetic sequence is −15, −33, −51, −69.

To find:

The nth term of the arithmetic sequence.

Solution:

We have,

−15, −33, −51, −69

Here,

First term: a = -15

Common difference is

$d = -33-(-15)$

$d = -33+15$

$d = -18$

Now, nth term  of an arithmetic sequence is

$a_n=a+(n-1)d$

Substitute a=-15 and d=-18.

$a_n=-15+(n-1)(-18)$

$a_n=-15-18n+18$

$a_n=-18n+3$

Therefore, the nth term of the given arithmetic sequence is $a_n=-18n+3$.